Abstract We consider a retailer selling two complementary products. The products are demanded individually or jointly. The retailer uses a continuous review ( Q , r ) policy to manage the inventory of each product. The customers arrive according to a Poisson process and unmet demands are lost. We aim to calculate the optimal policy parameters which maximize the expected profit rate. A shortage of one product might result in a lost sale of its complementary product, even if this product is in stock. This fact complicates the analysis. We rely on a simulation-based optimization approach to derive the optimal parameters of the ( Q , r ) policy for each product. Our results reveal that the maximum profit rate is attained when all customers demand both products, i.e., the bundle of complementary products. In addition, we observe that when the demand rate is low, the interaction between product demands has significant impact on the expected profit rate, and this effect becomes even more prominent when the unit lost sale costs are low and the unit holding costs are high. We derive the analytical properties of a single-product inventory system based on which an efficient approximation algorithm is developed.

中文翻译：

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针对具有相互关联需求的两种互补产品的持续审查政策

摘要 我们考虑销售两种互补产品的零售商。这些产品是单独或共同需求的。零售商使用持续审查 ( Q , r ) 策略来管理每个产品的库存。客户根据泊松过程到达，未满足的需求就会丢失。我们的目标是计算最大化预期利润率的最优政策参数。一种产品的短缺可能会导致其补充产品的销售损失，即使该产品有库存。这一事实使分析复杂化。我们依靠基于模拟的优化方法来推导出每个产品的 (Q, r) 策略的最佳参数。我们的结果表明，当所有客户都需要两种产品，即互补产品的捆绑时，可以获得最大的利润率。此外，我们观察到，当需求率低时，产品需求之间的交互作用对预期利润率有显着影响，当单位销售损失成本低且单位持有成本高时，这种影响更加突出。我们推导出了单一产品库存系统的分析特性，在此基础上开发了一种有效的近似算法。